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1 in 27, or 1 in 128, or 0.0078125.

Note: the stated equation is 1 in 27, not 1 in 28, because the question said "same results 8 times in a row". If the question said "heads, 8 times in a row", then the answer would be 1 in 28, but since it said "same results", you have to consider that the second through the eighth flip must match the first flip, and that is 1 in 27.

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Q: What are the odds of coin flip having the same results 8 times in a row?
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